Outbreaks of hepatitis, typhoid, cholera or dysentery are "inevitable" in Syria and its neighbours this summer, while cases of measles and other infections are already growing because of the country's broken health system and increasing numbers of displaced people, the World Health Organisation (WHO) has warned.

More than a third of Syria's public hospitals are out of action, in some areas 70% of health workers have fled and 4.25 million internally displaced Syrians are living in overcrowded, insanitary conditions, it said. Shortages of safe drinking water and disruption to vaccination programmes are increasing the risks.

With thousands of Syrians crossing the borders each day, diseases already prevalent inside Syria are being transmitted to neighbouring countries, according to the WHO's regional office for the eastern Mediterranean, just days ahead of new United Nations appeals for funds to combat the humanitarian crisis."All the risk factors that enhance the transmission of communicable diseases in emergencies are present in the current crisis in Syria and its neighbouring countries," said Jaouad Mahjour, its director for communicable diseases.

"We are anticipating a number of public health risks from water-borne diseases, specifically hepatitis, typhoid, cholera and dysentery. Given the scale of population movement both inside Syria and across borders, together with deteriorating environmental health conditions, outbreaks are inevitable."

There have been significant increases of acute watery diarrhoea and hepatitis. Typhoid is also on the rise. Vaccination campaigns against measles have been hit and cutaneous leishmaniasis, a disease transmitted to humans through sand fly bites already endemic in parts of Syria, especially Aleppo, is spreading.

Measles, tuberculosis and cutaneous leishmaniasis have been reported among displaced Syrians in Jordan, Lebanon, Iraq and Turkey. Mahjour said: "Jordan had previously reported zero cases of measles for three years, and was planning to officially declare that it was measles-free. The situation will deteriorate if prevention and control measures are not scaled up soon."

His organisation is helping countries plan emergency mass vaccination programmes, train more people to provide frontline treatments, prepare emergency depots with medicines and medical supplies and set aside laboratories to identify diseases.

Nick Martlew, senior conflict and humanitarian advocacy adviser at Save the Children, said: "We're already seeing an impact on children's health, with increasing numbers suffering from conditions such as diarrhoea, hepatitis A and upper respiratory tract infections – all of which can be deadly if left untreated.

"We are especially concerned about the poorest families, because they are most likely to be living in overcrowded communal shelters with little or no access to clean water or adequate sanitation," said Martlew. "With every passing day the potential for an epidemic increases, and children are likely to bear the brunt of any disease outbreak. It is a huge concern."

On Friday, UN organisations including Unicef will be launching a new appeal to combat the growing crisis in Syria and with refugees in neighbouring countries. When the last appeal launched in January, Unicef asked for $195.8m (£128m) to fund the work until the end of this month. Nearly a third was for work inside Syria, the rest to help refugees in neighbouring countries. The new appeal will cover work until the end of the year.

Unicef said that, despite the disruption, funds so far had helped emergency vaccination programmes, with close to a million children having been inoculated against measles and 620,000 against polio. They also provided generators for water pumps, hygiene kits, high-energy biscuits, rehydration kits and water purification tablets.